The two words are pretty close in meaning. In most cases, can be used interchangeably.

Сейчас can perhaps be a bit more immediate than теперь. In many cases, сейчас = at this very moment, whereas теперь can sometimes be used to mean these days.
Он сейчас занимается спортом.At this moment he's doing sports. These days he does sports. Both are possible in the right context.
Он теперь занимается спортом.These days he does sports. This is the more likely interpretation.

Some English examples:

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"What are you doing now?" (at this moment)
Both are possible but I prefer сейчас.

"I live in Canada now" (ie. I didn't live there before)
Both are possible, but I have a strong preference for теперь.

What's the difference between теперь and сейчас? They apparently both mean now, but I'm guessing there's some difference in usage?

Some English examples:
"What are you doing now?" (at this moment)
"I live in Canada now" (ie. I didn't live there before)
"What do you want now?" (ie. expressing repetition/exasperation)

Would the two words be interchangeable in these cases?

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"теперь" in meaning 'now' has a connotation 'as opposed to what had place in past'
''теперь я живу в Канаде' - I lived somewhere else before, but in Canada now.
''сейчас я живу в Канаде' - neutral.
''теперь(сейчас) я снова живу в Канаде' - I lived somewhere else just before and had lived before that in Canada.

In the third example 'теперь' have a 'repetition' connotation, as if it were some similar questions before it, or if some conditions changed just before - 'что ты думаешь об этой проблеме теперь?' . 'сейчас' have not.

"теперь" in meaning 'now' has a connotation 'as opposed to what had place in past'
''теперь я живу в Канаде' - I lived somewhere else before, but in Canada now.
''сейчас я живу в Канаде' - neutral.
''теперь(сейчас) я снова живу в Канаде' - I lived somewhere else just before and had lived before that in Canada.

In the third example 'теперь' have a 'repetition' connotation, as if it were some similar questions before it, or if some conditions changed just before - 'что ты думаешь об этой проблеме теперь?' . 'сейчас' have not.

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Thanks everyone. One question though: "cновa" apparently indicates that you lived somewhere else just before, but had previously lived in Canada. What are some other uses of that word?

Sorry, vox, but I disagree. In my opinion, the second sentence has exactly the same meaning as the first one....not mentioning some tiny nuances.
There is no reason to say 'сейчас я живу в Канаде', unless I lived somewhere else before.
Otherwise, сейчас might imply I am about to leave for some other place....

If I may summarize from the discussion above, сейчас can be fairly accurately translated as "right now" or "just now" and work the same in most contexts, while теперь means a 'generic' or 'broader' "now":

I live in Canada right now - Сейчас я живу в КанадеBoth imply that you have lived or plan to live somewhere else

When are you going to do it? - Right now/СейчасBoth mean "immediately" or "just a minute".

If I may summarize from the discussion above, сейчас can be fairly accurately translated as "right now" or "just now" and work the same in most contexts, while теперь means a 'generic' or 'broader' "now":

I live in Canada right now - Сейчас я живу в КанадеBoth imply that you have lived or plan to live somewhere else

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Теперь olny implies that you have lived somewhere else. It has a bit of "already" meaning, so to speak. The word is often coupled with уже (already). "Президент, теперь уже бывший..."

When are you going to do it? - Right now/СейчасBoth mean "immediately" or "just a minute".

"I told myself over and over again, 'He has just* fainted, he has just fainted.' But he was dead." (source) (... лишь потерял сознание...) *(или "he has simply/only/merely fainted")
"And then, quite suddenly, Ron is silent. She prays that he has just* fainted from the struggle, but she knows better. She lies quiet and listens to Ron Weasley die…" (source) (... лишь потерял сознание...)*(или "he has simply/only/merely fainted")
"Carefully, she laid two of her fingers on his artery. After a while she nodded."He's alive," she said, relieved. "He has just* fainted." (source) (... лишь потерял сознание...) *(или "he has simply/only/merely fainted")